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- Publisher Website: 10.1007/s10444-004-7637-9
- Scopus: eid_2-s2.0-33645770294
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Article: Generation of finite tight frames by Householder transformations
| Title | Generation of finite tight frames by Householder transformations |
|---|---|
| Authors | |
| Keywords | Condition number Frames Householder matrix Tight frame Tight frame matrix |
| Issue Date | 2006 |
| Citation | Advances in Computational Mathematics, 2006, v. 24, n. 1-4, p. 297-309 How to Cite? |
| Abstract | Finite tight frames are widely used for many applications. An important problem is to construct finite frames with prescribed norm for each vector in the tight frame. In this paper we provide a fast and simple algorithm for such a purpose. Our algorithm employs the Householder transformations. For a finite tight frame consisting of m vectors in ℝn or ℂn only O(nm) operations are needed. In addition, we also study the following question: Given a set of vectors in ℝn or ℂn, how many additional vectors, possibly with constraints, does one need to add in order to obtain a tight frame? © Springer 2006. |
| Persistent Identifier | http://hdl.handle.net/10722/363086 |
| ISSN | 2023 Impact Factor: 1.7 2023 SCImago Journal Rankings: 0.995 |
| DC Field | Value | Language |
|---|---|---|
| dc.contributor.author | Feng, De Jun | - |
| dc.contributor.author | Wang, Long | - |
| dc.contributor.author | Wang, Yang | - |
| dc.date.accessioned | 2025-10-10T07:44:30Z | - |
| dc.date.available | 2025-10-10T07:44:30Z | - |
| dc.date.issued | 2006 | - |
| dc.identifier.citation | Advances in Computational Mathematics, 2006, v. 24, n. 1-4, p. 297-309 | - |
| dc.identifier.issn | 1019-7168 | - |
| dc.identifier.uri | http://hdl.handle.net/10722/363086 | - |
| dc.description.abstract | Finite tight frames are widely used for many applications. An important problem is to construct finite frames with prescribed norm for each vector in the tight frame. In this paper we provide a fast and simple algorithm for such a purpose. Our algorithm employs the Householder transformations. For a finite tight frame consisting of m vectors in ℝ<sup>n</sup> or ℂ<sup>n</sup> only O(nm) operations are needed. In addition, we also study the following question: Given a set of vectors in ℝ<sup>n</sup> or ℂ<sup>n</sup>, how many additional vectors, possibly with constraints, does one need to add in order to obtain a tight frame? © Springer 2006. | - |
| dc.language | eng | - |
| dc.relation.ispartof | Advances in Computational Mathematics | - |
| dc.subject | Condition number | - |
| dc.subject | Frames | - |
| dc.subject | Householder matrix | - |
| dc.subject | Tight frame | - |
| dc.subject | Tight frame matrix | - |
| dc.title | Generation of finite tight frames by Householder transformations | - |
| dc.type | Article | - |
| dc.description.nature | link_to_subscribed_fulltext | - |
| dc.identifier.doi | 10.1007/s10444-004-7637-9 | - |
| dc.identifier.scopus | eid_2-s2.0-33645770294 | - |
| dc.identifier.volume | 24 | - |
| dc.identifier.issue | 1-4 | - |
| dc.identifier.spage | 297 | - |
| dc.identifier.epage | 309 | - |